Block #617,810

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/5/2014, 7:32:41 AM · Difficulty 10.9465 · 6,190,248 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf6529574abcdae9e940679b281ea9ad2648f8e83745d92a716a195b80a89fb6

View on Chainz ↗

Height

#617,810

Difficulty

10.946463

Transactions

Size

18.06 KB

Version

Bits

0af24b69

Nonce

802,990,432

Timestamp

7/5/2014, 7:32:41 AM

Confirmations

6,190,248

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7deacfc755641bb4ba3537a2af63aabb57cb42d934785edc90ab01701993dc1a

Transactions (4)

Coinbase4dad17159a1499…5d7524fea59233

1 in → 1 out8.5300 XPM116 B

ANSXnLY2…Sd25TjkD

2a3641a40e5552…1944770ec5749f

120 in → 2 out1004.2000 XPM17.42 KB

ALRPoJ4o…uihG3rKo AYAB2STP…YQwXbXYh

ca7f31357a17d7…2bec51d9f8d65d

1 in → 2 out8.3400 XPM226 B

Aa2rPQFc…3XZfScsP AVeoKEHW…hGQjMhDV

454661d94a0086…5290ed928b90d1

1 in → 2 out8.3400 XPM227 B

AUcvmo2P…BgMhcJri AGzX6zrq…2sUqUFQZ

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.

1.049 × 10⁹⁸(99-digit number)

10498831881660566279…33635878968098940799

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

1.049 × 10⁹⁸(99-digit number)

10498831881660566279…33635878968098940799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.049 × 10⁹⁸(99-digit number)

10498831881660566279…33635878968098940801

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

2.099 × 10⁹⁸(99-digit number)

20997663763321132559…67271757936197881599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.099 × 10⁹⁸(99-digit number)

20997663763321132559…67271757936197881601

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

4.199 × 10⁹⁸(99-digit number)

41995327526642265119…34543515872395763199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.199 × 10⁹⁸(99-digit number)

41995327526642265119…34543515872395763201

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

8.399 × 10⁹⁸(99-digit number)

83990655053284530239…69087031744791526399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.399 × 10⁹⁸(99-digit number)

83990655053284530239…69087031744791526401

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

1.679 × 10⁹⁹(100-digit number)

16798131010656906047…38174063489583052799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.679 × 10⁹⁹(100-digit number)

16798131010656906047…38174063489583052801

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

3.359 × 10⁹⁹(100-digit number)

33596262021313812095…76348126979166105599

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 #617,810

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