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Block #1,166,412

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/23/2015, 6:36:03 AM Β· Difficulty 10.9341 Β· 5,677,703 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
be7591ee5c7829a0fd0d8f270c38b311b28b8f91c54285fa80a6922084fa73c3
View on Chainz β†—

Height

#1,166,412

Difficulty

10.934079

Transactions

2

Size

1.43 KB

Version

2

Bits

0aef1fcb

Nonce

90,366,009

Timestamp

7/23/2015, 6:36:03 AM

Confirmations

5,677,703

Mined by

⛏️ P2SHAPqqvvapn2YHS7kThQUW8xKd5oqF4rc8Np

Merkle Root

e5d8f920325ee5c33c3072b381ad9c74f05030600a9d66c4b667cc39794068fd
Transactions (2)
Coinbase42e2c3a97cbf21…7fe7d3fd3ec77b
1 in β†’ 1 out8.3700 XPM109 B
APqqvvap…qF4rc8Np
d98809b82bde66…51bf968d7f78e1
8 in β†’ 2 out1248.0622 XPM1.24 KB
ALh4DDXS…11M8HJLoAYDRQ2yL…P2FK8J3E
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.

1.993 Γ— 10⁹⁸(99-digit number)
19936709635004101395…11462859903242076159
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
1.993 Γ— 10⁹⁸(99-digit number)
19936709635004101395…11462859903242076159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.993 Γ— 10⁹⁸(99-digit number)
19936709635004101395…11462859903242076161
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
3.987 Γ— 10⁹⁸(99-digit number)
39873419270008202790…22925719806484152319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.987 Γ— 10⁹⁸(99-digit number)
39873419270008202790…22925719806484152321
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
7.974 Γ— 10⁹⁸(99-digit number)
79746838540016405581…45851439612968304639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.974 Γ— 10⁹⁸(99-digit number)
79746838540016405581…45851439612968304641
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
1.594 Γ— 10⁹⁹(100-digit number)
15949367708003281116…91702879225936609279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.594 Γ— 10⁹⁹(100-digit number)
15949367708003281116…91702879225936609281
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
3.189 Γ— 10⁹⁹(100-digit number)
31898735416006562232…83405758451873218559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.189 Γ— 10⁹⁹(100-digit number)
31898735416006562232…83405758451873218561
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
6.379 Γ— 10⁹⁹(100-digit number)
63797470832013124465…66811516903746437119
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:57,997,295 XPMΒ·at block #6,844,114 Β· updates every 60s
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