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Block #1,680,981

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2016, 2:02:37 AM Β· Difficulty 10.7118 Β· 5,164,221 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a75cefe4e07b9dabfef9439e79ffaada1e9fd31badef634aaf6e4c11be36b1c6
View on Chainz β†—

Height

#1,680,981

Difficulty

10.711804

Transactions

1

Size

199 B

Version

2

Bits

0ab638d0

Nonce

1,195,247,401

Timestamp

7/20/2016, 2:02:37 AM

Confirmations

5,164,221

Mined by

⛏️ P2SHAR2kUFCFLAUhBqkdx1HsmyeywibMLm8u8e

Merkle Root

e52720a03dd358f999f5540a4c9c55c0b365caec99ddd7c937c2d7735fc375af
Transactions (1)
Coinbasee52720a03dd358…c2d7735fc375af
1 in β†’ 1 out8.7000 XPM109 B
AR2kUFCF…bMLm8u8e
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.

5.059 Γ— 10⁹⁴(95-digit number)
50590274841170200454…36073057458778537279
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
5.059 Γ— 10⁹⁴(95-digit number)
50590274841170200454…36073057458778537279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.059 Γ— 10⁹⁴(95-digit number)
50590274841170200454…36073057458778537281
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
1.011 Γ— 10⁹⁡(96-digit number)
10118054968234040090…72146114917557074559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.011 Γ— 10⁹⁡(96-digit number)
10118054968234040090…72146114917557074561
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
2.023 Γ— 10⁹⁡(96-digit number)
20236109936468080181…44292229835114149119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.023 Γ— 10⁹⁡(96-digit number)
20236109936468080181…44292229835114149121
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
4.047 Γ— 10⁹⁡(96-digit number)
40472219872936160363…88584459670228298239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.047 Γ— 10⁹⁡(96-digit number)
40472219872936160363…88584459670228298241
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
8.094 Γ— 10⁹⁡(96-digit number)
80944439745872320727…77168919340456596479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.094 Γ— 10⁹⁡(96-digit number)
80944439745872320727…77168919340456596481
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:58,006,049 XPMΒ·at block #6,845,201 Β· updates every 60s
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