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Block #1,084,515

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/31/2015, 5:37:06 PM Β· Difficulty 10.7657 Β· 5,740,515 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3c19b0a21a14f30a8c018c8c3c67891e62ca266ba892e1da5355e09f22dfbde1
View on Chainz β†—

Height

#1,084,515

Difficulty

10.765717

Transactions

1

Size

199 B

Version

2

Bits

0ac40604

Nonce

660,002,163

Timestamp

5/31/2015, 5:37:06 PM

Confirmations

5,740,515

Mined by

⛏️ P2SHATwJ91MsUGH8HPPc1ra2sGhf2AEPwmDUUW

Merkle Root

f5008118bcbbaa7ebe385de1028a33c47ef0804b3b6ea010d39f33c265171d21
Transactions (1)
Coinbasef5008118bcbbaa…9f33c265171d21
1 in β†’ 1 out8.6100 XPM109 B
ATwJ91Ms…EPwmDUUW
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.

2.372 Γ— 10⁹⁴(95-digit number)
23726846919505576501…66737497501039522559
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
2.372 Γ— 10⁹⁴(95-digit number)
23726846919505576501…66737497501039522559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.372 Γ— 10⁹⁴(95-digit number)
23726846919505576501…66737497501039522561
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
4.745 Γ— 10⁹⁴(95-digit number)
47453693839011153002…33474995002079045119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.745 Γ— 10⁹⁴(95-digit number)
47453693839011153002…33474995002079045121
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
9.490 Γ— 10⁹⁴(95-digit number)
94907387678022306005…66949990004158090239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.490 Γ— 10⁹⁴(95-digit number)
94907387678022306005…66949990004158090241
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
1.898 Γ— 10⁹⁡(96-digit number)
18981477535604461201…33899980008316180479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.898 Γ— 10⁹⁡(96-digit number)
18981477535604461201…33899980008316180481
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
3.796 Γ— 10⁹⁡(96-digit number)
37962955071208922402…67799960016632360959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.796 Γ— 10⁹⁡(96-digit number)
37962955071208922402…67799960016632360961
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:57,844,323 XPMΒ·at block #6,825,029 Β· updates every 60s
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