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Block #2,132,076

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/25/2017, 1:17:08 PM Β· Difficulty 10.9102 Β· 4,709,706 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1c9cfe1622b5dc76a4b4e0f52a3bc16dc882e75d62cfb4117a8cfe591304b22a
View on Chainz β†—

Height

#2,132,076

Difficulty

10.910200

Transactions

1

Size

200 B

Version

2

Bits

0ae902d9

Nonce

160,307,397

Timestamp

5/25/2017, 1:17:08 PM

Confirmations

4,709,706

Mined by

⛏️ P2SHATeqJUjMpztyemuB6za1Ziq7rKgbSkgwhc

Merkle Root

35cf769731c5b9c0a9c5bc79e9580fcfbdf185cd427be70469923fa1e92ca4e5
Transactions (1)
Coinbase35cf769731c5b9…923fa1e92ca4e5
1 in β†’ 1 out8.3900 XPM109 B
ATeqJUjM…gbSkgwhc
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.

1.811 Γ— 10⁹⁷(98-digit number)
18111498210249847850…07751902158694195199
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
1.811 Γ— 10⁹⁷(98-digit number)
18111498210249847850…07751902158694195199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.811 Γ— 10⁹⁷(98-digit number)
18111498210249847850…07751902158694195201
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
3.622 Γ— 10⁹⁷(98-digit number)
36222996420499695700…15503804317388390399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.622 Γ— 10⁹⁷(98-digit number)
36222996420499695700…15503804317388390401
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
7.244 Γ— 10⁹⁷(98-digit number)
72445992840999391400…31007608634776780799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.244 Γ— 10⁹⁷(98-digit number)
72445992840999391400…31007608634776780801
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
1.448 Γ— 10⁹⁸(99-digit number)
14489198568199878280…62015217269553561599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.448 Γ— 10⁹⁸(99-digit number)
14489198568199878280…62015217269553561601
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
2.897 Γ— 10⁹⁸(99-digit number)
28978397136399756560…24030434539107123199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.897 Γ— 10⁹⁸(99-digit number)
28978397136399756560…24030434539107123201
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
5.795 Γ— 10⁹⁸(99-digit number)
57956794272799513120…48060869078214246399
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:57,978,633 XPMΒ·at block #6,841,781 Β· updates every 60s
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