Block #2,913,240

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 11/7/2018, 4:45:42 AM · Difficulty 11.4968 · 3,928,424 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

69c3a376bff8f77022d6456c92aa8e5291280ff0285488cb76b2637d60ea4db4

View on Chainz ↗

Height

#2,913,240

Difficulty

11.496825

Transactions

Size

811 B

Version

Bits

0b7f2ff0

Nonce

1,018,851,956

Timestamp

11/7/2018, 4:45:42 AM

Confirmations

3,928,424

Mined by

⛏️ P2SHAYX18gYeUNQJYsvCYQme7WyhcDasd1iAdu

Merkle Root

885b1ec7e8bbc1151f9a2d5bdabca2aded715fa3f27bb9280b9f046096e95532

Transactions (3)

Coinbase32fa07d4f92886…b741310f3daae7

1 in → 1 out7.5700 XPM110 B

AYX18gYe…asd1iAdu

ccb0f06c6f3514…5dc234b970d7d7

2 in → 2 out14.9900 XPM304 B

ARh926hd…WYcLM5kw Ae7fmgVK…km4EKVdJ

232afbc63bb041…2a0748590f3ae9

2 in → 2 out14.9900 XPM307 B

AZW9Zv5x…mVPYfgfr AV3UWQyt…WsWYVfej

Prime Chain Origin

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

3.061 × 10⁹⁵(96-digit number)

30617640807668541350…36584754876782591999

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

3.061 × 10⁹⁵(96-digit number)

30617640807668541350…36584754876782591999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.061 × 10⁹⁵(96-digit number)

30617640807668541350…36584754876782592001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

6.123 × 10⁹⁵(96-digit number)

61235281615337082700…73169509753565183999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.123 × 10⁹⁵(96-digit number)

61235281615337082700…73169509753565184001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.224 × 10⁹⁶(97-digit number)

12247056323067416540…46339019507130367999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.224 × 10⁹⁶(97-digit number)

12247056323067416540…46339019507130368001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.449 × 10⁹⁶(97-digit number)

24494112646134833080…92678039014260735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.449 × 10⁹⁶(97-digit number)

24494112646134833080…92678039014260736001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.898 × 10⁹⁶(97-digit number)

48988225292269666160…85356078028521471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.898 × 10⁹⁶(97-digit number)

48988225292269666160…85356078028521472001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.797 × 10⁹⁶(97-digit number)

97976450584539332320…70712156057042943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

9.797 × 10⁹⁶(97-digit number)

97976450584539332320…70712156057042944001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★★☆

Rarity

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,913,240

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