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Block #2,283,416

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2017, 10:58:09 AM Β· Difficulty 10.9556 Β· 4,557,978 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1f5f9be0f7564219fde44bf4c505cdf512f13ae7e427ad9aa515abc5bd33683e
View on Chainz β†—

Height

#2,283,416

Difficulty

10.955577

Transactions

1

Size

200 B

Version

2

Bits

0af4a0b0

Nonce

892,288,686

Timestamp

9/5/2017, 10:58:09 AM

Confirmations

4,557,978

Mined by

⛏️ P2SHAJhnc329imB4jPBcPbx3K1f4zFkQHTQ3TG

Merkle Root

261f37b00aaca2d9ac3dd5cac3e2cf0fff20a5d83eeb2f13db641c93155a421a
Transactions (1)
Coinbase261f37b00aaca2…641c93155a421a
1 in β†’ 1 out8.3200 XPM109 B
AJhnc329…kQHTQ3TG
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.

1.397 Γ— 10⁹⁸(99-digit number)
13974729476378609653…01739596395344035839
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
1.397 Γ— 10⁹⁸(99-digit number)
13974729476378609653…01739596395344035839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.397 Γ— 10⁹⁸(99-digit number)
13974729476378609653…01739596395344035841
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
2.794 Γ— 10⁹⁸(99-digit number)
27949458952757219306…03479192790688071679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.794 Γ— 10⁹⁸(99-digit number)
27949458952757219306…03479192790688071681
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
5.589 Γ— 10⁹⁸(99-digit number)
55898917905514438613…06958385581376143359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.589 Γ— 10⁹⁸(99-digit number)
55898917905514438613…06958385581376143361
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
1.117 Γ— 10⁹⁹(100-digit number)
11179783581102887722…13916771162752286719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.117 Γ— 10⁹⁹(100-digit number)
11179783581102887722…13916771162752286721
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
2.235 Γ— 10⁹⁹(100-digit number)
22359567162205775445…27833542325504573439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.235 Γ— 10⁹⁹(100-digit number)
22359567162205775445…27833542325504573441
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
4.471 Γ— 10⁹⁹(100-digit number)
44719134324411550890…55667084651009146879
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:57,975,524 XPMΒ·at block #6,841,393 Β· updates every 60s
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