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Block #615,597

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/4/2014, 3:04:39 AM Β· Difficulty 10.9407 Β· 6,209,665 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f65207ce9fb68a1e3f5856edafbbabab5f8a8e5bbac9e373e377de01f030b882
View on Chainz β†—

Height

#615,597

Difficulty

10.940743

Transactions

2

Size

582 B

Version

2

Bits

0af0d487

Nonce

104,696,386

Timestamp

7/4/2014, 3:04:39 AM

Confirmations

6,209,665

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

114b68c5b0079b5035199f5de9c42e0ef72c2db52c1fd1d4bfbf8243e7a510da
Transactions (2)
Coinbasec4b70b572f0a2e…fa8ed836043b13
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
2f19455853e63d…2c40c0450425e0
2 in β†’ 2 out14.0370 XPM374 B
ANwP8Hmi…gkrFk6t9Aeayyu6e…t4WrCqvu
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.

7.094 Γ— 10⁹⁸(99-digit number)
70940250020928721045…94285192813446348799
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
7.094 Γ— 10⁹⁸(99-digit number)
70940250020928721045…94285192813446348799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.094 Γ— 10⁹⁸(99-digit number)
70940250020928721045…94285192813446348801
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
1.418 Γ— 10⁹⁹(100-digit number)
14188050004185744209…88570385626892697599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.418 Γ— 10⁹⁹(100-digit number)
14188050004185744209…88570385626892697601
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
2.837 Γ— 10⁹⁹(100-digit number)
28376100008371488418…77140771253785395199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.837 Γ— 10⁹⁹(100-digit number)
28376100008371488418…77140771253785395201
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
5.675 Γ— 10⁹⁹(100-digit number)
56752200016742976836…54281542507570790399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.675 Γ— 10⁹⁹(100-digit number)
56752200016742976836…54281542507570790401
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
1.135 Γ— 10¹⁰⁰(101-digit number)
11350440003348595367…08563085015141580799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.135 Γ— 10¹⁰⁰(101-digit number)
11350440003348595367…08563085015141580801
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
2.270 Γ— 10¹⁰⁰(101-digit number)
22700880006697190734…17126170030283161599
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
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