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Block #1,680,605

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2016, 8:42:18 PM Β· Difficulty 10.7087 Β· 5,162,319 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2d290993f44213c2289a99de0e35800cb5ff7e555043a0442a7c02eef40f5f38
View on Chainz β†—

Height

#1,680,605

Difficulty

10.708727

Transactions

1

Size

200 B

Version

2

Bits

0ab56f26

Nonce

1,438,443,651

Timestamp

7/19/2016, 8:42:18 PM

Confirmations

5,162,319

Mined by

⛏️ P2SHAT4Hiyg6gxmv1zkQ7aCZYuiwZDFo3n2B8E

Merkle Root

42921e432444d2aaa46ce2dc271d1a520161e0f725cc74cea3e0a260c678c309
Transactions (1)
Coinbase42921e432444d2…e0a260c678c309
1 in β†’ 1 out8.7100 XPM109 B
AT4Hiyg6…Fo3n2B8E
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.

1.052 Γ— 10⁹⁷(98-digit number)
10527170251408029168…33078996748540385279
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
1.052 Γ— 10⁹⁷(98-digit number)
10527170251408029168…33078996748540385279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.052 Γ— 10⁹⁷(98-digit number)
10527170251408029168…33078996748540385281
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
2.105 Γ— 10⁹⁷(98-digit number)
21054340502816058337…66157993497080770559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.105 Γ— 10⁹⁷(98-digit number)
21054340502816058337…66157993497080770561
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
4.210 Γ— 10⁹⁷(98-digit number)
42108681005632116674…32315986994161541119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.210 Γ— 10⁹⁷(98-digit number)
42108681005632116674…32315986994161541121
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
8.421 Γ— 10⁹⁷(98-digit number)
84217362011264233348…64631973988323082239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.421 Γ— 10⁹⁷(98-digit number)
84217362011264233348…64631973988323082241
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
1.684 Γ— 10⁹⁸(99-digit number)
16843472402252846669…29263947976646164479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.684 Γ— 10⁹⁸(99-digit number)
16843472402252846669…29263947976646164481
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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