Block #1,469,824

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2016, 11:05:21 PM · Difficulty 10.7424 · 5,347,450 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2581a00c598c60be0543c044059a13677fc6e8ce7ac326faf169758d70f715fe

View on Chainz ↗

Height

#1,469,824

Difficulty

10.742403

Transactions

Size

2.04 KB

Version

Bits

0abe0e19

Nonce

1,280,702,283

Timestamp

2/23/2016, 11:05:21 PM

Confirmations

5,347,450

Mined by

⛏️ P2SHAb7DoKCmJBpL2yCPo8Med6mqZSvZ5Yq72w

Merkle Root

65c5797ae2f0f9aba50b4f7c6719ebb1ca7cc2841cff8f04e91c28d44fd139f3

Transactions (2)

Coinbasef4539f70aef7bc…86dfab7c27df18

1 in → 1 out8.6700 XPM110 B

Ab7DoKCm…vZ5Yq72w

14c3c1f83cd25e…48ad26ebd9a81c

1 in → 51 out52.8149 XPM1.85 KB

AL1F2M5H…mvLnjjFq ARbmELZZ…D2EmA9eK AQLBS8SQ…evTam6se ALzYMT8T…Td7EbSvY Acr54Uhg…FeYtSbEq

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.

9.678 × 10⁹⁵(96-digit number)

96784857008324163071…97326766379938335999

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

9.678 × 10⁹⁵(96-digit number)

96784857008324163071…97326766379938335999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.678 × 10⁹⁵(96-digit number)

96784857008324163071…97326766379938336001

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

1.935 × 10⁹⁶(97-digit number)

19356971401664832614…94653532759876671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.935 × 10⁹⁶(97-digit number)

19356971401664832614…94653532759876672001

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

3.871 × 10⁹⁶(97-digit number)

38713942803329665228…89307065519753343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.871 × 10⁹⁶(97-digit number)

38713942803329665228…89307065519753344001

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

7.742 × 10⁹⁶(97-digit number)

77427885606659330456…78614131039506687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.742 × 10⁹⁶(97-digit number)

77427885606659330456…78614131039506688001

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

1.548 × 10⁹⁷(98-digit number)

15485577121331866091…57228262079013375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.548 × 10⁹⁷(98-digit number)

15485577121331866091…57228262079013376001

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 #1,469,824

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