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Block #2,233,537

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/2/2017, 8:59:16 AM Β· Difficulty 10.9463 Β· 4,593,540 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7aadaef5c8514d0202a4caea9bdf22b19566dec1b502d406befdd202a38237fc
View on Chainz β†—

Height

#2,233,537

Difficulty

10.946300

Transactions

2

Size

1.14 KB

Version

2

Bits

0af240bf

Nonce

985,065,445

Timestamp

8/2/2017, 8:59:16 AM

Confirmations

4,593,540

Mined by

⛏️ P2SHAUFbwRBuiVBhdVkV7vUC9jn4Qx85brPwmX

Merkle Root

ce98ca66506ee9da5fb847f11be43dfae061de3233797499dd8545e0af31afe5
Transactions (2)
Coinbased7113ee015a8cd…b9bd39fa4f3684
1 in β†’ 1 out8.3400 XPM110 B
AUFbwRBu…85brPwmX
4076091dbf758e…88d8ce913b96ee
6 in β†’ 2 out3452.0404 XPM966 B
AMA49Cx2…gpm5Wn47AZAUpPRK…y6qkZdaT
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.

2.163 Γ— 10⁹⁷(98-digit number)
21631068032482252642…75450610197555302399
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
2.163 Γ— 10⁹⁷(98-digit number)
21631068032482252642…75450610197555302399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.163 Γ— 10⁹⁷(98-digit number)
21631068032482252642…75450610197555302401
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
4.326 Γ— 10⁹⁷(98-digit number)
43262136064964505285…50901220395110604799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.326 Γ— 10⁹⁷(98-digit number)
43262136064964505285…50901220395110604801
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
8.652 Γ— 10⁹⁷(98-digit number)
86524272129929010571…01802440790221209599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.652 Γ— 10⁹⁷(98-digit number)
86524272129929010571…01802440790221209601
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
1.730 Γ— 10⁹⁸(99-digit number)
17304854425985802114…03604881580442419199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.730 Γ— 10⁹⁸(99-digit number)
17304854425985802114…03604881580442419201
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
3.460 Γ— 10⁹⁸(99-digit number)
34609708851971604228…07209763160884838399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.460 Γ— 10⁹⁸(99-digit number)
34609708851971604228…07209763160884838401
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
6.921 Γ— 10⁹⁸(99-digit number)
69219417703943208457…14419526321769676799
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:57,860,800 XPMΒ·at block #6,827,076 Β· updates every 60s
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