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Block #2,123,041

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/19/2017, 12:49:38 AM Β· Difficulty 10.9160 Β· 4,718,788 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e5d2a27bb5a762d619b3f84b5877927af6e8bd2bb7a3a23b9d855a7bf4be0213
View on Chainz β†—

Height

#2,123,041

Difficulty

10.915985

Transactions

1

Size

242 B

Version

2

Bits

0aea7dff

Nonce

289,589,640

Timestamp

5/19/2017, 12:49:38 AM

Confirmations

4,718,788

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

6fa4c544a5f6b1399948c4deb2ffc0275e87c6095bb2b7f14a6c09d889f9baf8
Transactions (1)
Coinbase6fa4c544a5f6b1…6c09d889f9baf8
1 in β†’ 2 out8.3800 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

5.516 Γ— 10⁹⁡(96-digit number)
55161352141033727087…26545952530421509039
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
5.516 Γ— 10⁹⁡(96-digit number)
55161352141033727087…26545952530421509039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.516 Γ— 10⁹⁡(96-digit number)
55161352141033727087…26545952530421509041
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
1.103 Γ— 10⁹⁢(97-digit number)
11032270428206745417…53091905060843018079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.103 Γ— 10⁹⁢(97-digit number)
11032270428206745417…53091905060843018081
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
2.206 Γ— 10⁹⁢(97-digit number)
22064540856413490834…06183810121686036159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.206 Γ— 10⁹⁢(97-digit number)
22064540856413490834…06183810121686036161
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
4.412 Γ— 10⁹⁢(97-digit number)
44129081712826981669…12367620243372072319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.412 Γ— 10⁹⁢(97-digit number)
44129081712826981669…12367620243372072321
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
8.825 Γ— 10⁹⁢(97-digit number)
88258163425653963339…24735240486744144639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.825 Γ— 10⁹⁢(97-digit number)
88258163425653963339…24735240486744144641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,979,005 XPMΒ·at block #6,841,828 Β· updates every 60s
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