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Block #2,716,271

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/22/2018, 9:51:16 AM Β· Difficulty 11.6144 Β· 4,126,313 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
23248174088f1e36c52e98cd005bbfc265b62302b3abc0e582247983525842da
View on Chainz β†—

Height

#2,716,271

Difficulty

11.614373

Transactions

2

Size

2.15 KB

Version

2

Bits

0b9d4794

Nonce

217,964,868

Timestamp

6/22/2018, 9:51:16 AM

Confirmations

4,126,313

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

3a63fb629c29d355793eca0e25136bc087e9bda9a5076e00d8b685635946647b
Transactions (2)
Coinbased60e5ed084cf7f…51d8721085c0df
1 in β†’ 1 out7.4300 XPM109 B
AZtxQr2F…7grUWrUz
fb4d5fa7a8430d…6730f57ad158a3
13 in β†’ 2 out19068.8800 XPM1.95 KB
AT5cy2iR…mxX4tuFqAU4MBGBZ…vqkBE1Y2
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.

1.440 Γ— 10⁹²(93-digit number)
14403853081275406000…48433158940081678759
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
1.440 Γ— 10⁹²(93-digit number)
14403853081275406000…48433158940081678759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.440 Γ— 10⁹²(93-digit number)
14403853081275406000…48433158940081678761
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
2.880 Γ— 10⁹²(93-digit number)
28807706162550812000…96866317880163357519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.880 Γ— 10⁹²(93-digit number)
28807706162550812000…96866317880163357521
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
5.761 Γ— 10⁹²(93-digit number)
57615412325101624001…93732635760326715039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.761 Γ— 10⁹²(93-digit number)
57615412325101624001…93732635760326715041
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
1.152 Γ— 10⁹³(94-digit number)
11523082465020324800…87465271520653430079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.152 Γ— 10⁹³(94-digit number)
11523082465020324800…87465271520653430081
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
2.304 Γ— 10⁹³(94-digit number)
23046164930040649600…74930543041306860159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.304 Γ— 10⁹³(94-digit number)
23046164930040649600…74930543041306860161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.609 Γ— 10⁹³(94-digit number)
46092329860081299201…49861086082613720319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,985,100 XPMΒ·at block #6,842,583 Β· updates every 60s
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