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Block #1,015,627

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/14/2015, 9:20:27 AM Β· Difficulty 10.7277 Β· 5,787,735 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
622ed0a19f9ed43767438ba5e4a1285c7df2fea8cc212e8032e34819c5d4d5c7
View on Chainz β†—

Height

#1,015,627

Difficulty

10.727695

Transactions

2

Size

432 B

Version

2

Bits

0aba4a35

Nonce

1,928,206,677

Timestamp

4/14/2015, 9:20:27 AM

Confirmations

5,787,735

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8c010a395c452d97eec183b8b682b9f0272031c028bc22d0f13c5a32418ba147
Transactions (2)
Coinbase70d39b830b8b38…fd4745973497e0
1 in β†’ 1 out8.6900 XPM116 B
ANSXnLY2…Sd25TjkD
9b52708c9a65d4…d9e0be88f7b286
1 in β†’ 2 out5.8914 XPM226 B
AGhLpCaq…Q2cWhfgVAZZ5QsQX…AsWyVsdY
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.

6.813 Γ— 10⁹⁡(96-digit number)
68131419225878691393…34432435350706831039
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
6.813 Γ— 10⁹⁡(96-digit number)
68131419225878691393…34432435350706831039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.813 Γ— 10⁹⁡(96-digit number)
68131419225878691393…34432435350706831041
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
1.362 Γ— 10⁹⁢(97-digit number)
13626283845175738278…68864870701413662079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.362 Γ— 10⁹⁢(97-digit number)
13626283845175738278…68864870701413662081
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
2.725 Γ— 10⁹⁢(97-digit number)
27252567690351476557…37729741402827324159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.725 Γ— 10⁹⁢(97-digit number)
27252567690351476557…37729741402827324161
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
5.450 Γ— 10⁹⁢(97-digit number)
54505135380702953114…75459482805654648319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.450 Γ— 10⁹⁢(97-digit number)
54505135380702953114…75459482805654648321
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
1.090 Γ— 10⁹⁷(98-digit number)
10901027076140590622…50918965611309296639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.090 Γ— 10⁹⁷(98-digit number)
10901027076140590622…50918965611309296641
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
2.180 Γ— 10⁹⁷(98-digit number)
21802054152281181245…01837931222618593279
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:57,670,932 XPMΒ·at block #6,803,361 Β· updates every 60s
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