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Block #1,613,790

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/4/2016, 1:45:30 PM Β· Difficulty 10.5964 Β· 5,227,111 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
602fab1c5c7cc70e341e37512e4c9320b0bcf9233cccd5f7603a0cd54b4ce652
View on Chainz β†—

Height

#1,613,790

Difficulty

10.596371

Transactions

1

Size

200 B

Version

2

Bits

0a98abc1

Nonce

1,030,898,336

Timestamp

6/4/2016, 1:45:30 PM

Confirmations

5,227,111

Mined by

⛏️ P2SHATUpLR1QMmiYPHwoYqPnER1Y8ArDfXkfwB

Merkle Root

2b928e67c043692fd4a1825cc3b62492bd8313b24e3cf3fcdeea932b6acf64b9
Transactions (1)
Coinbase2b928e67c04369…ea932b6acf64b9
1 in β†’ 1 out8.8900 XPM109 B
ATUpLR1Q…rDfXkfwB
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.

1.602 Γ— 10⁹⁢(97-digit number)
16026552051926051609…81278833723934411519
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
1.602 Γ— 10⁹⁢(97-digit number)
16026552051926051609…81278833723934411519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.602 Γ— 10⁹⁢(97-digit number)
16026552051926051609…81278833723934411521
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
3.205 Γ— 10⁹⁢(97-digit number)
32053104103852103218…62557667447868823039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.205 Γ— 10⁹⁢(97-digit number)
32053104103852103218…62557667447868823041
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
6.410 Γ— 10⁹⁢(97-digit number)
64106208207704206437…25115334895737646079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.410 Γ— 10⁹⁢(97-digit number)
64106208207704206437…25115334895737646081
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
1.282 Γ— 10⁹⁷(98-digit number)
12821241641540841287…50230669791475292159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.282 Γ— 10⁹⁷(98-digit number)
12821241641540841287…50230669791475292161
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
2.564 Γ— 10⁹⁷(98-digit number)
25642483283081682574…00461339582950584319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.564 Γ— 10⁹⁷(98-digit number)
25642483283081682574…00461339582950584321
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:57,971,558 XPMΒ·at block #6,840,900 Β· updates every 60s
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