Block #1,516,252

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2016, 6:03:52 PM · Difficulty 10.6012 · 5,308,655 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

360df43a6d32cf6f85894919d602d0e8e7480bc788e827a4e9acd22d4c5446d8

View on Chainz ↗

Height

#1,516,252

Difficulty

10.601200

Transactions

Size

11.31 KB

Version

Bits

0a99e843

Nonce

135,281,521

Timestamp

3/28/2016, 6:03:52 PM

Confirmations

5,308,655

Mined by

⛏️ P2SHAFonJRRSXNscB88qWwUneRkQJUS3oKQAnj

Merkle Root

f0632c4e5c2401d1d0f487e1d6737bf1a0193590d8ef5fe4e5735cb3c98e0d94

Transactions (2)

Coinbase62228edbf9c4d5…fdf6c332bd06bc

1 in → 1 out9.0000 XPM109 B

AFonJRRS…S3oKQAnj

1e75020123a384…afd2277a96720f

1 in → 330 out202.4410 XPM11.11 KB

APKH9RPe…LUEGiGj5 AW9dmmRi…Nm2s6YtB AHUnFPcc…YB39UjTG APoPzX2Z…qxQXGXWe AYU6QUUw…eF2J5WU5

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.

1.244 × 10⁹⁷(98-digit number)

12446127252975817668…90530057717818531839

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

1.244 × 10⁹⁷(98-digit number)

12446127252975817668…90530057717818531839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.244 × 10⁹⁷(98-digit number)

12446127252975817668…90530057717818531841

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

2.489 × 10⁹⁷(98-digit number)

24892254505951635336…81060115435637063679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.489 × 10⁹⁷(98-digit number)

24892254505951635336…81060115435637063681

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

4.978 × 10⁹⁷(98-digit number)

49784509011903270672…62120230871274127359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.978 × 10⁹⁷(98-digit number)

49784509011903270672…62120230871274127361

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

9.956 × 10⁹⁷(98-digit number)

99569018023806541345…24240461742548254719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.956 × 10⁹⁷(98-digit number)

99569018023806541345…24240461742548254721

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

1.991 × 10⁹⁸(99-digit number)

19913803604761308269…48480923485096509439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.991 × 10⁹⁸(99-digit number)

19913803604761308269…48480923485096509441

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 #1,516,252

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