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Block #909,201

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/25/2015, 9:16:46 AM Β· Difficulty 10.9343 Β· 5,900,722 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
72fdb69a570da8bf0634a65d8f9039a3d501f1e97761bf8da2499d1a1802f0b5
View on Chainz β†—

Height

#909,201

Difficulty

10.934346

Transactions

2

Size

5.34 KB

Version

2

Bits

0aef3151

Nonce

51,371,255

Timestamp

1/25/2015, 9:16:46 AM

Confirmations

5,900,722

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0822d5996087cc2f77fcab061331aa392ad1dd77237d2cbb8f56523b7c8e936c
Transactions (2)
Coinbase2dedbba1cca215…36859f9a69682b
1 in β†’ 1 out8.5500 XPM116 B
ANSXnLY2…Sd25TjkD
c8fb2b3045b459…8edd9ce5de6ff7
35 in β†’ 2 out43644.9921 XPM5.13 KB
AN49sf7T…EgDikWEtAPa4a74n…pkePp7H4
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.477 Γ— 10⁹⁹(100-digit number)
34774008504120997928…30107604922365460479
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.477 Γ— 10⁹⁹(100-digit number)
34774008504120997928…30107604922365460479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.477 Γ— 10⁹⁹(100-digit number)
34774008504120997928…30107604922365460481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
6.954 Γ— 10⁹⁹(100-digit number)
69548017008241995857…60215209844730920959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.954 Γ— 10⁹⁹(100-digit number)
69548017008241995857…60215209844730920961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.390 Γ— 10¹⁰⁰(101-digit number)
13909603401648399171…20430419689461841919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.390 Γ— 10¹⁰⁰(101-digit number)
13909603401648399171…20430419689461841921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.781 Γ— 10¹⁰⁰(101-digit number)
27819206803296798342…40860839378923683839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.781 Γ— 10¹⁰⁰(101-digit number)
27819206803296798342…40860839378923683841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
5.563 Γ— 10¹⁰⁰(101-digit number)
55638413606593596685…81721678757847367679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.563 Γ— 10¹⁰⁰(101-digit number)
55638413606593596685…81721678757847367681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.112 Γ— 10¹⁰¹(102-digit number)
11127682721318719337…63443357515694735359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,723,470 XPMΒ·at block #6,809,922 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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