Block #1,216,424

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/1/2015, 12:33:21 AM · Difficulty 10.7275 · 5,600,941 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8791ab5924496c7fa304d57d2e77e856379230ff57a5c03d229476c479d617db

View on Chainz ↗

Height

#1,216,424

Difficulty

10.727501

Transactions

Size

868 B

Version

Bits

0aba3d7c

Nonce

1,427,949,589

Timestamp

9/1/2015, 12:33:21 AM

Confirmations

5,600,941

Mined by

⛏️ P2SHAQh4gQ3VPRtwVwNLY2qJWnVck56sBEA6Y4

Merkle Root

af1d902262cad1b40118b795f0a2456201789536ff6905ad8c951c8d4e7625df

Transactions (2)

Coinbase2e1d6450a60a1c…60e40e2714e09c

1 in → 1 out8.6900 XPM109 B

AQh4gQ3V…6sBEA6Y4

f6af203d674d26…b866a5ab5431e0

4 in → 2 out46.2363 XPM670 B

AHhem1Zi…ooRrsR7Y AGwxfFXK…jgS4tVMX

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.

2.237 × 10⁹²(93-digit number)

22374373504315243212…93998944724987149839

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

2.237 × 10⁹²(93-digit number)

22374373504315243212…93998944724987149839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.237 × 10⁹²(93-digit number)

22374373504315243212…93998944724987149841

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

4.474 × 10⁹²(93-digit number)

44748747008630486424…87997889449974299679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.474 × 10⁹²(93-digit number)

44748747008630486424…87997889449974299681

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

8.949 × 10⁹²(93-digit number)

89497494017260972849…75995778899948599359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.949 × 10⁹²(93-digit number)

89497494017260972849…75995778899948599361

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

1.789 × 10⁹³(94-digit number)

17899498803452194569…51991557799897198719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.789 × 10⁹³(94-digit number)

17899498803452194569…51991557799897198721

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

3.579 × 10⁹³(94-digit number)

35798997606904389139…03983115599794397439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.579 × 10⁹³(94-digit number)

35798997606904389139…03983115599794397441

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 #1,216,424

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