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Block #2,155,300

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/10/2017, 9:03:52 PM Β· Difficulty 10.9057 Β· 4,671,768 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c898fc783dc0c17af7d3f35328d9199b7e6ce8acebada98a16f58f4945cd9310
View on Chainz β†—

Height

#2,155,300

Difficulty

10.905680

Transactions

1

Size

200 B

Version

2

Bits

0ae7daa7

Nonce

1,666,993,937

Timestamp

6/10/2017, 9:03:52 PM

Confirmations

4,671,768

Mined by

⛏️ P2SHAKz1keEGEnUcZKFmfrr4zv8Ri4jtp6Nnz2

Merkle Root

ff0aaae2436a3def511541133468f0a773341e6f7e9d8209ffa1f3f862e5851c
Transactions (1)
Coinbaseff0aaae2436a3d…a1f3f862e5851c
1 in β†’ 1 out8.3900 XPM110 B
AKz1keEG…jtp6Nnz2
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.

3.311 Γ— 10⁹⁡(96-digit number)
33112441694301332052…61723703940879073279
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
3.311 Γ— 10⁹⁡(96-digit number)
33112441694301332052…61723703940879073279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.311 Γ— 10⁹⁡(96-digit number)
33112441694301332052…61723703940879073281
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
6.622 Γ— 10⁹⁡(96-digit number)
66224883388602664105…23447407881758146559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.622 Γ— 10⁹⁡(96-digit number)
66224883388602664105…23447407881758146561
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
1.324 Γ— 10⁹⁢(97-digit number)
13244976677720532821…46894815763516293119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.324 Γ— 10⁹⁢(97-digit number)
13244976677720532821…46894815763516293121
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
2.648 Γ— 10⁹⁢(97-digit number)
26489953355441065642…93789631527032586239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.648 Γ— 10⁹⁢(97-digit number)
26489953355441065642…93789631527032586241
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
5.297 Γ— 10⁹⁢(97-digit number)
52979906710882131284…87579263054065172479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.297 Γ— 10⁹⁢(97-digit number)
52979906710882131284…87579263054065172481
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
1.059 Γ— 10⁹⁷(98-digit number)
10595981342176426256…75158526108130344959
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:57,860,726 XPMΒ·at block #6,827,067 Β· updates every 60s
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