Block #1,252,453

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/25/2015, 6:07:06 AM · Difficulty 10.7835 · 5,565,025 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8eb7bd8fc366a687689f5891b098ad6dfeae45cf3fdfa9dcdb36abb120d34872

View on Chainz ↗

Height

#1,252,453

Difficulty

10.783533

Transactions

Size

908 B

Version

Bits

0ac89597

Nonce

1,885,542

Timestamp

9/25/2015, 6:07:06 AM

Confirmations

5,565,025

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

684e2b5017eba57ac30135bbf683c255710a748b18507d146ea36ddad119c152

Transactions (2)

Coinbaseed76bbfb618a82…aa984ee97320d9

1 in → 1 out8.6000 XPM116 B

AJCEY9yy…tg97E6zm

1bd12b830f49b1…da9aecf6600aa4

1 in → 16 out114.1835 XPM702 B

AdXaUrde…ZoizVcpy AKvfQFwC…VoCqRW3f AeRjKEPg…t7JtLopg APdbVByB…MbanfPYm AXLkjH6Q…9wXKhR9V

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.

5.588 × 10⁹⁴(95-digit number)

55884453385644531968…05874203407277888499

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

5.588 × 10⁹⁴(95-digit number)

55884453385644531968…05874203407277888499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.588 × 10⁹⁴(95-digit number)

55884453385644531968…05874203407277888501

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

1.117 × 10⁹⁵(96-digit number)

11176890677128906393…11748406814555776999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.117 × 10⁹⁵(96-digit number)

11176890677128906393…11748406814555777001

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

2.235 × 10⁹⁵(96-digit number)

22353781354257812787…23496813629111553999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.235 × 10⁹⁵(96-digit number)

22353781354257812787…23496813629111554001

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

4.470 × 10⁹⁵(96-digit number)

44707562708515625575…46993627258223107999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.470 × 10⁹⁵(96-digit number)

44707562708515625575…46993627258223108001

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

8.941 × 10⁹⁵(96-digit number)

89415125417031251150…93987254516446215999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.941 × 10⁹⁵(96-digit number)

89415125417031251150…93987254516446216001

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

1.788 × 10⁹⁶(97-digit number)

17883025083406250230…87974509032892431999

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 #1,252,453

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