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Block #681,078

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/17/2014, 5:16:20 AM Β· Difficulty 10.9620 Β· 6,146,231 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f908e1f2c4cfb3d8c1b9b604663e84628af70d9fcc1ebfa0323d6885f9bedaae
View on Chainz β†—

Height

#681,078

Difficulty

10.962031

Transactions

3

Size

659 B

Version

2

Bits

0af647a4

Nonce

38,961,663

Timestamp

8/17/2014, 5:16:20 AM

Confirmations

6,146,231

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7db641a7976cf9bcfb4182eec612ff3e97ea23fd0fb6b367f031f49435769a08
Transactions (3)
Coinbase93eb1c58d49a0a…143d99450b9738
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
50b4ebfea3369d…568f27a54ddb8c
1 in β†’ 2 out3.8760 XPM226 B
AL86cz8Y…kKfWsz7kAKLuG6Tv…XcP2RFiM
36d8053a512d37…57f51c3182e18a
1 in β†’ 2 out2.2472 XPM226 B
AX5AJLd9…M3mEZCGVAYU1Ynxb…6LNs2ZYM
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.477 Γ— 10⁹⁷(98-digit number)
54770296729230863495…58512709360595967999
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.477 Γ— 10⁹⁷(98-digit number)
54770296729230863495…58512709360595967999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.477 Γ— 10⁹⁷(98-digit number)
54770296729230863495…58512709360595968001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.095 Γ— 10⁹⁸(99-digit number)
10954059345846172699…17025418721191935999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.095 Γ— 10⁹⁸(99-digit number)
10954059345846172699…17025418721191936001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.190 Γ— 10⁹⁸(99-digit number)
21908118691692345398…34050837442383871999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.190 Γ— 10⁹⁸(99-digit number)
21908118691692345398…34050837442383872001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.381 Γ— 10⁹⁸(99-digit number)
43816237383384690796…68101674884767743999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.381 Γ— 10⁹⁸(99-digit number)
43816237383384690796…68101674884767744001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
8.763 Γ— 10⁹⁸(99-digit number)
87632474766769381592…36203349769535487999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.763 Γ— 10⁹⁸(99-digit number)
87632474766769381592…36203349769535488001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,862,584 XPMΒ·at block #6,827,308 Β· updates every 60s
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