Block #3,037,471

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/3/2019, 8:56:42 PM · Difficulty 11.0074 · 3,804,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cec0a02fe8e5a5b9cc8372a40fcb080e9f6eb9361a60cf05a0171daba775151b

View on Chainz ↗

Height

#3,037,471

Difficulty

11.007381

Transactions

Size

1.49 KB

Version

Bits

0b01e3b1

Nonce

456,138,424

Timestamp

2/3/2019, 8:56:42 PM

Confirmations

3,804,832

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

ff69c9e41bd1a453753a5741874af7f92a1cff76603ff198a06d1d75aa5d8954

Transactions (5)

Coinbase0f04ea3b167b51…d2271ee64f9466

1 in → 1 out8.2800 XPM109 B

AbXwmGxD…4XXYP765

53eb3692d66b0e…649596131451a4

1 in → 2 out8.3000 XPM192 B

AbXwmGxD…4XXYP765 ALB2Fo4H…SodNKWDE

1f152120b0b0cf…ae0768245503f7

1 in → 2 out8.2100 XPM193 B

AbXwmGxD…4XXYP765 AWLhispt…YegP97ro

f13a5f60f619a1…1122b17a868236

4 in → 2 out20.8019 XPM605 B

AbXwmGxD…4XXYP765 AWu6SVKR…fD2XKYmk

f9e75e2e2bd7a8…426d065ec644b7

2 in → 2 out14.3874 XPM341 B

AXgNzcfF…AhQqtGB2 AbXwmGxD…4XXYP765

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.

9.978 × 10⁹⁴(95-digit number)

99781243048520061103…48143938031170119679

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

9.978 × 10⁹⁴(95-digit number)

99781243048520061103…48143938031170119679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.978 × 10⁹⁴(95-digit number)

99781243048520061103…48143938031170119681

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

1.995 × 10⁹⁵(96-digit number)

19956248609704012220…96287876062340239359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.995 × 10⁹⁵(96-digit number)

19956248609704012220…96287876062340239361

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

3.991 × 10⁹⁵(96-digit number)

39912497219408024441…92575752124680478719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.991 × 10⁹⁵(96-digit number)

39912497219408024441…92575752124680478721

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

7.982 × 10⁹⁵(96-digit number)

79824994438816048882…85151504249360957439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.982 × 10⁹⁵(96-digit number)

79824994438816048882…85151504249360957441

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

1.596 × 10⁹⁶(97-digit number)

15964998887763209776…70303008498721914879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.596 × 10⁹⁶(97-digit number)

15964998887763209776…70303008498721914881

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

3.192 × 10⁹⁶(97-digit number)

31929997775526419553…40606016997443829759

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 #3,037,471

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