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Block #902,926

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/20/2015, 5:48:12 PM Β· Difficulty 10.9393 Β· 5,892,979 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d0c3dc2165bf81eed1b0848b205d0dbf8b0f00c462305dc8675db15f6bfb51a7
View on Chainz β†—

Height

#902,926

Difficulty

10.939307

Transactions

2

Size

1.00 KB

Version

2

Bits

0af07666

Nonce

154,717,373

Timestamp

1/20/2015, 5:48:12 PM

Confirmations

5,892,979

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8b413226225314cc1e127849efda5d587d837979af33b95155bc5266ed9d16c1
Transactions (2)
Coinbaseeb1331d37743d3…c7f355cc94b0fd
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
26eaf63e4321a4…ca9b63df78ed31
5 in β†’ 2 out508.9807 XPM817 B
AGaE6x9K…TA3okV85AR3NsN6L…zoMC9e95
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.

1.294 Γ— 10⁹⁷(98-digit number)
12945415678254147535…08291103001888890879
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
1.294 Γ— 10⁹⁷(98-digit number)
12945415678254147535…08291103001888890879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.294 Γ— 10⁹⁷(98-digit number)
12945415678254147535…08291103001888890881
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
2.589 Γ— 10⁹⁷(98-digit number)
25890831356508295070…16582206003777781759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.589 Γ— 10⁹⁷(98-digit number)
25890831356508295070…16582206003777781761
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
5.178 Γ— 10⁹⁷(98-digit number)
51781662713016590141…33164412007555563519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.178 Γ— 10⁹⁷(98-digit number)
51781662713016590141…33164412007555563521
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
1.035 Γ— 10⁹⁸(99-digit number)
10356332542603318028…66328824015111127039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.035 Γ— 10⁹⁸(99-digit number)
10356332542603318028…66328824015111127041
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
2.071 Γ— 10⁹⁸(99-digit number)
20712665085206636056…32657648030222254079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.071 Γ— 10⁹⁸(99-digit number)
20712665085206636056…32657648030222254081
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
4.142 Γ— 10⁹⁸(99-digit number)
41425330170413272113…65315296060444508159
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:57,611,324 XPMΒ·at block #6,795,904 Β· updates every 60s
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