Block #754,154

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/6/2014, 9:23:34 AM · Difficulty 10.9699 · 6,052,262 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

21e4c803e191f1dd31372389889ec7c7ad13ce8429ca46cc668387d6079b3a9b

View on Chainz ↗

Height

#754,154

Difficulty

10.969904

Transactions

Size

1.34 KB

Version

Bits

0af84b9c

Nonce

1,753,369,368

Timestamp

10/6/2014, 9:23:34 AM

Confirmations

6,052,262

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1ef204851e7e806228a468cf92fed877e602c0738814af51192238159c48f739

Transactions (5)

Coinbase0827bf22f6ca2f…45915e8d4f191b

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

4299569f6d7b30…a057898a9781c3

1 in → 2 out8.3100 XPM193 B

AZwJmUvM…qKucBVTg AMN6qDkt…VuvvTq6f

5c57bbca804477…4004cb91236570

3 in → 2 out23.3627 XPM524 B

AXf14f7B…XaySGXLU AWcWtrTe…cSH2v1rN

27a560b347683d…a0e452c63fa48c

1 in → 2 out5.7196 XPM226 B

ATjwywoV…ga9eRXwi ASzjSRZn…9p6N372x

d10204657cb005…523cde908e34e6

1 in → 2 out3.8610 XPM226 B

AMHmq8gf…uxskoCcY AGFD3Ho1…J57ViRCn

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.

9.785 × 10⁹⁵(96-digit number)

97850208314886865139…72135971127591614719

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

9.785 × 10⁹⁵(96-digit number)

97850208314886865139…72135971127591614719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.785 × 10⁹⁵(96-digit number)

97850208314886865139…72135971127591614721

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

1.957 × 10⁹⁶(97-digit number)

19570041662977373027…44271942255183229439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.957 × 10⁹⁶(97-digit number)

19570041662977373027…44271942255183229441

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

3.914 × 10⁹⁶(97-digit number)

39140083325954746055…88543884510366458879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.914 × 10⁹⁶(97-digit number)

39140083325954746055…88543884510366458881

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

7.828 × 10⁹⁶(97-digit number)

78280166651909492111…77087769020732917759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.828 × 10⁹⁶(97-digit number)

78280166651909492111…77087769020732917761

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

1.565 × 10⁹⁷(98-digit number)

15656033330381898422…54175538041465835519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.565 × 10⁹⁷(98-digit number)

15656033330381898422…54175538041465835521

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 #754,154

Cookie Preferences