Block #1,212,205

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/28/2015, 6:34:06 PM · Difficulty 10.7511 · 5,614,922 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b808c6a6c87fdf72f713bbea6e617517000a82b182a6b50f0208ec46ec68b6e1

View on Chainz ↗

Height

#1,212,205

Difficulty

10.751070

Transactions

Size

2.04 KB

Version

Bits

0ac04622

Nonce

513,835,363

Timestamp

8/28/2015, 6:34:06 PM

Confirmations

5,614,922

Mined by

⛏️ P2SHAKxtJNAsBPEL4mZfiN47fj2iYQiV6P9SC3

Merkle Root

2e414048a757561f557057bf8261818a92c398b5edc12c5b3af12edd8a65d8a6

Transactions (2)

Coinbase7b38d60f56198b…8587e163d8a0e0

1 in → 1 out8.6600 XPM110 B

AKxtJNAs…iV6P9SC3

52de0af7e9cc39…017d09c2c793dc

1 in → 51 out40.7868 XPM1.85 KB

AbbuTGrt…GTMXU6w6 AZCL29vD…3xkKKRUD ASf56EmJ…urQdVeD5 ARMMxjj1…3aJAcKcN AXhAgNHv…CZzxwD4g

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.

1.292 × 10⁹³(94-digit number)

12920008691967350371…39227176757001572439

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

1.292 × 10⁹³(94-digit number)

12920008691967350371…39227176757001572439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.292 × 10⁹³(94-digit number)

12920008691967350371…39227176757001572441

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

2.584 × 10⁹³(94-digit number)

25840017383934700742…78454353514003144879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.584 × 10⁹³(94-digit number)

25840017383934700742…78454353514003144881

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

5.168 × 10⁹³(94-digit number)

51680034767869401484…56908707028006289759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.168 × 10⁹³(94-digit number)

51680034767869401484…56908707028006289761

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

1.033 × 10⁹⁴(95-digit number)

10336006953573880296…13817414056012579519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.033 × 10⁹⁴(95-digit number)

10336006953573880296…13817414056012579521

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

2.067 × 10⁹⁴(95-digit number)

20672013907147760593…27634828112025159039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.067 × 10⁹⁴(95-digit number)

20672013907147760593…27634828112025159041

Verify on FactorDB ↗Wolfram Alpha ↗

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

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 — 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

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 × 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 #1,212,205

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