Block #372,753

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2014, 8:12:20 PM · Difficulty 10.4257 · 6,434,612 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea8feba174ec5ebfec8fa82449da8fdd69ea4239509cc732e9608fd3300a2345

View on Chainz ↗

Height

#372,753

Difficulty

10.425734

Transactions

Size

1.39 KB

Version

Bits

0a6cfce1

Nonce

168,841

Timestamp

1/23/2014, 8:12:20 PM

Confirmations

6,434,612

Mined by

Ac2JYASPQD7vWBs42nkRqpCmFvtcBL5PEW

Merkle Root

cb882f896fa502b6f67a5a76ea887318043a233d517fe5f3b692d74ba0b95701

Transactions (5)

Coinbase22743b15ad98f2…21dafa441a0ba9

1 in → 2 out9.2300 XPM131 B

Ac2JYASP…tcBL5PEW AJno7LX2…vo4wdWtY

7c8d709f03d1dc…63639dc237d4bf

3 in → 2 out27.6800 XPM521 B

AdEXaN4v…gTtGYj6K AFtSNtk8…8Aw3ciMi

296338bba253e6…18af520cf8e7d9

1 in → 2 out9.1400 XPM226 B

AXtoco72…7oSHYMRt Ab3J4ipo…GaHrWuuW

83a4b53e7016fb…12bd46cdabf29d

1 in → 2 out9.1400 XPM225 B

APUrHFBe…QHG1pxNq AT9ThTBi…A27eShUU

257c8d056931d9…180451aaf2c145

1 in → 2 out9.1400 XPM226 B

AYY1J62Q…SySGVTY3 ATgAgYKV…vJbELgd3

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.

8.577 × 10⁹⁵(96-digit number)

85772193691214930624…47594479201865530879

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

8.577 × 10⁹⁵(96-digit number)

85772193691214930624…47594479201865530879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.577 × 10⁹⁵(96-digit number)

85772193691214930624…47594479201865530881

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

1.715 × 10⁹⁶(97-digit number)

17154438738242986124…95188958403731061759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.715 × 10⁹⁶(97-digit number)

17154438738242986124…95188958403731061761

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

3.430 × 10⁹⁶(97-digit number)

34308877476485972249…90377916807462123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.430 × 10⁹⁶(97-digit number)

34308877476485972249…90377916807462123521

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

6.861 × 10⁹⁶(97-digit number)

68617754952971944499…80755833614924247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.861 × 10⁹⁶(97-digit number)

68617754952971944499…80755833614924247041

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

1.372 × 10⁹⁷(98-digit number)

13723550990594388899…61511667229848494079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.372 × 10⁹⁷(98-digit number)

13723550990594388899…61511667229848494081

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 #372,753

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