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Block #2,617,636

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/17/2018, 7:16:23 AM Β· Difficulty 11.2299 Β· 4,186,146 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a64f322b336f09d3af4a4bb224715d1ed12f20cfd34c1265ff63ce63a8a4170f
View on Chainz β†—

Height

#2,617,636

Difficulty

11.229922

Transactions

2

Size

91.74 KB

Version

2

Bits

0b3adc25

Nonce

360,096,849

Timestamp

4/17/2018, 7:16:23 AM

Confirmations

4,186,146

Mined by

⛏️ P2SHAS9i42VpZGdYhFkkJE79jmoCSAT7EqhvjP

Merkle Root

e9a7a76dac536d5b0ad14a59e1a1a1e9301f98e5dad79fa0c2a77a312ba66695
Transactions (2)
Coinbaseef1b0252b0236d…cb7574e8ec2775
1 in β†’ 1 out8.8600 XPM110 B
AS9i42Vp…T7EqhvjP
967d7217c82b49…0a62e0ae073896
633 in β†’ 1 out650.0000 XPM91.54 KB
ALPF8J52…Hjw4BMsG
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.

1.299 Γ— 10⁹⁷(98-digit number)
12992867216691866471…79987142114305187839
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
1.299 Γ— 10⁹⁷(98-digit number)
12992867216691866471…79987142114305187839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.299 Γ— 10⁹⁷(98-digit number)
12992867216691866471…79987142114305187841
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
2.598 Γ— 10⁹⁷(98-digit number)
25985734433383732943…59974284228610375679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.598 Γ— 10⁹⁷(98-digit number)
25985734433383732943…59974284228610375681
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
5.197 Γ— 10⁹⁷(98-digit number)
51971468866767465887…19948568457220751359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.197 Γ— 10⁹⁷(98-digit number)
51971468866767465887…19948568457220751361
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
1.039 Γ— 10⁹⁸(99-digit number)
10394293773353493177…39897136914441502719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.039 Γ— 10⁹⁸(99-digit number)
10394293773353493177…39897136914441502721
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
2.078 Γ— 10⁹⁸(99-digit number)
20788587546706986355…79794273828883005439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.078 Γ— 10⁹⁸(99-digit number)
20788587546706986355…79794273828883005441
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
4.157 Γ— 10⁹⁸(99-digit number)
41577175093413972710…59588547657766010879
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:57,674,296 XPMΒ·at block #6,803,781 Β· updates every 60s
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