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Block #2,127,669

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/22/2017, 4:11:01 AM Β· Difficulty 10.9179 Β· 4,705,775 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b35ee01b1d82e1540d2e8fbf0c0e9867694889450a8fece42ec1eb168ea57685
View on Chainz β†—

Height

#2,127,669

Difficulty

10.917924

Transactions

1

Size

243 B

Version

2

Bits

0aeafd0a

Nonce

593,985,403

Timestamp

5/22/2017, 4:11:01 AM

Confirmations

4,705,775

Mined by

⛏️ P2SHAMqQLF2btsYPo7Jp7xi3EuC8tcDPrNk1cy

Merkle Root

2ad5a4c0df468b24584f73ae35072577ee2f34d07dcc4e11084b57dba8a2ed5d
Transactions (1)
Coinbase2ad5a4c0df468b…4b57dba8a2ed5d
1 in β†’ 2 out8.3800 XPM152 B
AMqQLF2b…DPrNk1cyAXbk7f7A…Tx7JECPG
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.

2.191 Γ— 10⁹⁢(97-digit number)
21916926471187226222…60320866623939295039
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
2.191 Γ— 10⁹⁢(97-digit number)
21916926471187226222…60320866623939295039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.191 Γ— 10⁹⁢(97-digit number)
21916926471187226222…60320866623939295041
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
4.383 Γ— 10⁹⁢(97-digit number)
43833852942374452445…20641733247878590079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.383 Γ— 10⁹⁢(97-digit number)
43833852942374452445…20641733247878590081
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
8.766 Γ— 10⁹⁢(97-digit number)
87667705884748904891…41283466495757180159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.766 Γ— 10⁹⁢(97-digit number)
87667705884748904891…41283466495757180161
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
1.753 Γ— 10⁹⁷(98-digit number)
17533541176949780978…82566932991514360319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.753 Γ— 10⁹⁷(98-digit number)
17533541176949780978…82566932991514360321
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
3.506 Γ— 10⁹⁷(98-digit number)
35067082353899561956…65133865983028720639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.506 Γ— 10⁹⁷(98-digit number)
35067082353899561956…65133865983028720641
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:57,911,750 XPMΒ·at block #6,833,443 Β· updates every 60s
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