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Block #2,636,800

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 5:26:45 PM Β· Difficulty 11.4022 Β· 4,205,194 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e46a035e8ce429a563ceab57d65e83a9185769a336bac66ee1d72c29fb4dc0d2
View on Chainz β†—

Height

#2,636,800

Difficulty

11.402161

Transactions

1

Size

200 B

Version

2

Bits

0b66f404

Nonce

837,068,759

Timestamp

4/29/2018, 5:26:45 PM

Confirmations

4,205,194

Mined by

⛏️ P2SHAHy5SEXbmUGQcgEQ36ro2g9PZNLY7WgF7z

Merkle Root

1a29bb4a23bbf77cdce6e215c5b9ca92c9730183071daaff39165ed3c91847c2
Transactions (1)
Coinbase1a29bb4a23bbf7…165ed3c91847c2
1 in β†’ 1 out7.6800 XPM109 B
AHy5SEXb…LY7WgF7z
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.

1.483 Γ— 10⁹⁷(98-digit number)
14836077483201966525…97580893509035505919
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
1.483 Γ— 10⁹⁷(98-digit number)
14836077483201966525…97580893509035505919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.483 Γ— 10⁹⁷(98-digit number)
14836077483201966525…97580893509035505921
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
2.967 Γ— 10⁹⁷(98-digit number)
29672154966403933051…95161787018071011839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.967 Γ— 10⁹⁷(98-digit number)
29672154966403933051…95161787018071011841
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
5.934 Γ— 10⁹⁷(98-digit number)
59344309932807866103…90323574036142023679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.934 Γ— 10⁹⁷(98-digit number)
59344309932807866103…90323574036142023681
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
1.186 Γ— 10⁹⁸(99-digit number)
11868861986561573220…80647148072284047359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.186 Γ— 10⁹⁸(99-digit number)
11868861986561573220…80647148072284047361
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
2.373 Γ— 10⁹⁸(99-digit number)
23737723973123146441…61294296144568094719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.373 Γ— 10⁹⁸(99-digit number)
23737723973123146441…61294296144568094721
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
4.747 Γ— 10⁹⁸(99-digit number)
47475447946246292882…22588592289136189439
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:57,980,340 XPMΒ·at block #6,841,993 Β· updates every 60s
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